Which of the following is NOT a conclusion of the Central Limit Theorem? Choose the correct answer below. A. The mean of all sample means is the population mean mu. B. The standard deviation of all sample means is the population standard deviation divided by the square root of the sample size. C. The distribution of the sample data will approach a normal distribution as the sample size increases. D. The distribution of the sample means x overbar will, as the sample size increases, approach a normal distribution.

Question

Mathematics

Steven Stephenson

23 July, 13:37

Which of the following is NOT a conclusion of the Central Limit Theorem? Choose the correct answer below. A. The mean of all sample means is the population mean mu. B. The standard deviation of all sample means is the population standard deviation divided by the square root of the sample size. C. The distribution of the sample data will approach a normal distribution as the sample size increases. D. The distribution of the sample means x overbar will, as the sample size increases, approach a normal distribution.

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Answers (1)

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Alani Lawson · Answer 1

The distribution of the sample data will approach a normal distribution as the sample size increases.

Step-by-step explanation:

Central limit theorem states that the mean of all samples from the same population will be almost equal to the mean of the population, if the large sample size from a population, is given with a finite level of variance.

So, here Option C is not correct conclusion of central limit theorem - The distribution of the sample data will approach a normal distribution as the sample size increases.

We can say that the average of sample mean tends to be normal but not the sample data.